It doesn't mean there is no 'server' component. It's supposed to mean that the devs don't have to worry about the underlying server infrastructure that is running their code. They simply specify the code and the conditions under which it gets executed, and the serverless service takes care of running it.

> For that, I think Functions-as-a-service makes more sense.

For internal documents I've written, I position FaaS as one category of Serverless services (which includes others like Database as a Service (DBaaS), etc.).

I've always seen it to mean cases where the code owner is not responsible for designating or managing individual servers, but instead they just deploy their code and the cloud provider is responsible for scaling based on incoming load.

In that model things like AWS Lambda and Google Cloud Functions are considered serverless, but so are Elastic Beanstalk, App Engine and Cloud Run.

Managing your own individual servers in something like EC2 or Cloud Compute is definitely something I would not consider serverless, and I think most people would agree with that.